Properties

Label 349830.o
Number of curves $4$
Conductor $349830$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("o1")
 
E.isogeny_class()
 

Elliptic curves in class 349830.o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
349830.o1 349830o4 \([1, -1, 0, -16188795, -25011558675]\) \(133345896593725369/340006815000\) \(1196396858978731215000\) \([2]\) \(29491200\) \(2.9209\)  
349830.o2 349830o2 \([1, -1, 0, -1404675, -58920939]\) \(87109155423289/49979073600\) \(175863553410559809600\) \([2, 2]\) \(14745600\) \(2.5743\)  
349830.o3 349830o1 \([1, -1, 0, -917955, 337366485]\) \(24310870577209/114462720\) \(402764981867089920\) \([2]\) \(7372800\) \(2.2278\) \(\Gamma_0(N)\)-optimal
349830.o4 349830o3 \([1, -1, 0, 5591925, -474518979]\) \(5495662324535111/3207841648920\) \(-11287572788413202388120\) \([2]\) \(29491200\) \(2.9209\)  

Rank

sage: E.rank()
 

The elliptic curves in class 349830.o have rank \(0\).

Complex multiplication

The elliptic curves in class 349830.o do not have complex multiplication.

Modular form 349830.2.a.o

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - q^{5} - q^{8} + q^{10} - 4 q^{11} + q^{16} + 6 q^{17} - 4 q^{19} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.